Problem: Solve for $x$ and $y$ using elimination. ${4x+2y = 30}$ ${5x-3y = 21}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $2$ ${12x+6y = 90}$ $10x-6y = 42$ Add the top and bottom equations together. $22x = 132$ $\dfrac{22x}{{22}} = \dfrac{132}{{22}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {4x+2y = 30}\thinspace$ to find $y$ ${4}{(6)}{ + 2y = 30}$ $24+2y = 30$ $24{-24} + 2y = 30{-24}$ $2y = 6$ $\dfrac{2y}{{2}} = \dfrac{6}{{2}}$ ${y = 3}$ You can also plug ${x = 6}$ into $\thinspace {5x-3y = 21}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ - 3y = 21}$ ${y = 3}$